How can I generate a repetition of impulse response when I feed the system with repetition of pulses?

I have the transfer function for a system and I want to generate a repetition of pulses as the input to the system and output the impulse response of the input pulses. The impulse response should be a repetition of the system impulse response.

Answer 1

[MathWorks Support Team]

We can use the Control System Toolbox to do this. 

The following code generates the system from the transfer function using 'tf' function

close all, clear all, clc
t=[0:.2e-3:1];             % Time vector
C=1e-2; L=20e-4; R=80e-3;       % System parameters
a=1; b=[L*C R*C 1];             % Denominators and numerators
sys=tf([a],[b])                 % Transfer function
impulse(sys)                    % Just a single pulse

Then we can generate the repetition of pulses and invoke the system impulse response using 'lsim' function.

% Generate input pulses
dt = 0.0002;                      %Sample rate
tend = 2.5;                       %Simulation period
t = 0:dt:tend;
period = 0.5;                     %Period of the input pulses
u = zeros(length(t),1);
for i=1:length(t)
    if rem(t(i),0.5)==0
        u(i)=1;
    end
end

% Invoke the system response
% sysd = c2d(sys,dt);             % Continuous to discrete system conversion.
[y yt] = lsim(sys,u,t);
y = y/dt;                         % Normalize with sample time.

% Plot the input and the output.
subplot(2,1,1);
plot(t,u);
title('Input');
subplot(2,1,2);
plot(yt,y);
title('Impulse Responce');